Let O be the origin. Let $\overline{\mathrm{OP}}=x \hat{\mathrm{i}}+y \hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overline{\mathrm{PQ}}=\sqrt{20} \overline{\mathrm{OQ}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 x \hat{\mathrm{k}}, x, y \in \mathrm{R}, x>0$, be such that $\overline{\mathrm{PQ}}=\sqrt{20}$ and the vector $\overline{\mathrm{OP}}$ is perpendicular to $\overline{\mathrm{OQ}}$. If $\overline{\mathrm{OR}}=3 \hat{\mathrm{i}}+z \hat{\mathrm{j}}-7 \hat{\mathrm{k}}, z \in \mathrm{R}$, is coplanar with $\overline{\mathrm{OP}}$ and $\overline{\mathrm{OQ}}$, then the value of $x^2+y^2+z^2$ is equal to